1 How to improve students' understanding of mathematics
Effective supplement helps students to understand correctly.
Mathematics reading comprehension has its particularity. The language in mathematics is always very concise, and some mathematical concepts and quantitative relations are usually hidden. When reading a math text, primary school students should supplement or expand the information and meaning provided by the topic through their own math knowledge in order to fully understand it.
There is such a problem: Xiaoling sells two clothes, and each one sells 60 yuan. 1 piece earned 20%, and one piece lost 20%. Is it profit or loss? After communication, I have the following ideas: ① One earns 20% and the other loses 20%. Isn't that balance? ② Earning 20% means 20% more, 60×( 1+20%), and losing 20% means 20% less, 60×( 1-20%). In order to help students understand the topic correctly, I communicate with students: "What do you mean by earning 20%?" "20% more." Students already know that earning 20% means earning 20% more. "Who is the 20% more than who? Can you complete this information? " "The price is 20% higher than the cost." "I also found that the price has been told and only the cost is needed." Obviously, when the text is incomplete, it will often hinder students' correct understanding of the meaning, and "supplementary information" is a good way to solve the problem.
Generous giving helps students to study effectively.
When students think and explore independently, their thinking ability will be effectively improved and their knowledge will be more profound. In the process of independent thinking and exploration, there will be various kinds of production, either wrong or correct and innovative. Last semester, I had an open class, "Relationship between perimeter and area of rectangle and square". "Use two iron wires with a length of16m to form a square and a rectangle respectively. Who is the bigger area of a square or a rectangle? Why? " This is my planned independent investigation. At the beginning, I did this: slide show-students think and answer independently (teachers patrol to understand students' problem-solving situation: methods, directions, etc. )-Feedback and communication.
When giving feedback, students raise their hands actively. One student found that other students were at a loss when using physical projection analysis. I'll give you about 2 minutes to watch this classmate's problem-solving process by yourself, and then this classmate will re-introduce his ideas. As a result, the students' voice just fell and the audience applauded. Imagine: when students are "at a loss", I have no temporary time for students to calm down and read and understand. Can I be suddenly enlightened? Can it make * * * sounds? Learn to be insightful when teaching, and give students time to calm down and read and think when necessary, so that the space for communication will become wider and wider.
2 mathematics interest teaching
Follow the teaching rules and make a teaching plan that conforms to the all-round development of primary school students' body and mind.
(A) the principle of adaptability, the structural level of knowledge should be consistent with students' cognitive level.
Teachers should pay attention to cultivating students' interest in learning in the usual mathematics teaching, and turn all kinds of knowledge into knowledge that conforms to students' normal cognitive habits in a gradient way. For example, all kinds of Olympiad competitions popular in primary school mathematics teaching. In fact, most of these questions are high-math questions, which are far beyond the normal understanding of students and inconsistent with their knowledge structure. In this way, they will find mathematics difficult to learn and have some fears, which will easily dampen their enthusiasm for learning.
(B) the principle of development, classroom teaching knowledge structure from easy to difficult, and gradually reflect the breadth and depth.
The principle of development means that mathematics classroom teaching should always combine students' own personal experience and cognition of nature, and the knowledge in the classroom should conform to students' cognitive characteristics, not too difficult or too simple. In learning, we should combine theory with real life problems and solve some practical problems with mathematics, so that students can feel that they have gained something and feel the happiness brought by learning. In this way, students not only master knowledge, but also are eager to learn more new knowledge, thus laying a foundation for the future classroom, teaching will become active and students' attention will be more concentrated. This is the scientific education model.
Teachers use a variety of teaching methods to stimulate students' interest in learning and effectively improve the teaching effect.
Let students experience different successes in different learning processes.
Everyone is eager for success and likes it. Mathematics class should make students feel the joy of success, so that they will work hard for success. Teachers can set gradient problems according to different teaching situations and students' ability to learn knowledge, so that students can solve them independently, so that everyone can succeed easily and feel successful. Mathematics knowledge is continuous and systematic, and teachers should understand teaching strategies step by step. Only when students perceive the happiness of success will they be eager for success.
Actively praise and encourage every student to enjoy success and share happiness.
Good students are boasted, not taught. In our classroom, we should grasp the competitive psychology of primary school students and cultivate their sense of honor. Therefore, in the teaching process, teachers can group students. When students make progress, teachers should give positive evaluation and praise in time, such as various stickers and math cards completed by teachers and students, so as not to dampen their enthusiasm for learning.
3 Mathematical thinking training
Mathematics is a science that needs high problem-solving skills.
Historically, mathematics is full of all kinds of problems and solutions. China's Nine Chapters Arithmetic appears in the form of problems and algorithms to solve them. In Europe, Euclid's geometry originally appeared in the form of deduction, but it was also full of problems and their solutions. The Greeks also left three famous geometric drawing problems. During the Italian Renaissance, mathematics was very prosperous, and mathematicians asked each other questions and sought answers as a form of challenge. In modern mathematics, people have made progress in their research, but they have also left many questions and conjectures for future generations. The solution of Fermat's last theorem is considered by mathematicians to be a very important event. Now people are still talking about many important issues, such as the zero point of Riemannian function, Poincare conjecture (which is said to have been proved) and so on. Mathematics makes progress by constantly solving problems and constantly generating new ones. This method of solving problems comes from creative mathematical thinking. Mathematicians invented imaginary numbers when solving cubic algebraic equations. When discussing whether algebraic equations can be solved by roots, Galois developed group theory, and the achievement of creative achievements must rely on the in-depth grasp and in-depth study of outstanding achievements of predecessors.
In our teaching work, we must let students master the basic learning content and thinking methods. Cultivate the spirit of in-depth and hard study. For excellent students, you can arrange some difficult problems, but you must not ask them to do things that are not available at present (such as solving historical problems in number theory), let alone do things that have been proved impossible (such as three major problems of geometric drawing), so as not to waste time and energy. You can't engage in sea tactics, simply memorize ready-made problem-solving methods, but ignore the training of mathematical thinking and the creative ability to find ways to solve problems by yourself. Mathematical olympiad is beneficial, but it is not appropriate to pay attention to these two aspects and make olympiad younger.
Mathematics is a rational science and an example of rational thinking.
It is said that some primary and middle school students regard mathematics as a subject of memorizing formulas, which is completely misunderstood. Of course, you need to remember in the process of learning mathematics, and sometimes you have to remember it well and say it without thinking, such as multiplication tables. But mathematics is a science of rational thinking and rigorous logical structure. We should not only know what it is, but also know why it is. The simplest formula also has its origin. The area of a rectangle is equal to the product of two side lengths, which is obtained from the experience of measuring the area.
Based on this empirical fact, we can prove a lot of things, so we can demonstrate the formulas of triangle, parallelogram, trapezoid and other graphic areas. "Gousan, Gusi and Xian Wu" is a special case of Pythagorean theorem, so such an important theorem must be proved, and it can also be obtained by calculating the area (the proof in ancient China is much simpler than that in Euclid geometry). Mathematics is not satisfied with individual things and phenomena. Another example is that /2 is an irrational number, and many steps are still incomplete. The fact that there is no cycle cannot explain the problem, because these steps are still limited, and this matter can only be established after strict proof. The process of demonstration, that is, the process of further understanding and revealing the internal relations, is an important means for students to improve their mathematics quality. Only when you understand it can you remember it firmly, and even if you forget it, you will interpret it yourself.
4 new ideas of mathematics classroom teaching
Strengthen the practicality of mathematics materials and make the classroom come alive.
Classroom teaching is the main position for students to learn scientific and cultural knowledge, and it is also the main channel for students to carry out ideological and moral education. So our mathematics can't be divorced from life and reality. This is the essence of the current educational reform, which requires us to think about what practical examples this knowledge is related to and where it is used in our lives before preparing for each class. Try to replace boring examples with examples that students like in actual situations; If you can find hands-on learning, let the students spell-divide-draw-play-speak; If you practice imitation and reproduce practical application, use it in conjunction with book practice. In short, "come from life and go back to life". For example, when teaching "Understanding of Circle", let students cite round objects in life to make them feel "circle", and then demonstrate several monkeys running on bicycles through multimedia. The wheels are triangle, rectangle, square, trapezoid and circle.
Let the students guess who runs fastest, and then the media will demonstrate the course of the competition. Finally, ask students why monkeys riding round wheels run first, so that students can understand why the wheels of bicycles are round, make them feel that learning mathematics is very useful, spontaneously generate interest in exploration, sprout a strong thirst for knowledge of "self-need" and be willing to innovate. Let students know more about mathematics knowledge and skills, not only from the relaxed and simple classroom, but also from the real life around them.
Cultivate students' application consciousness and solve problems rationally.
Students' application consciousness is mainly manifested in "recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in the real world;" In the face of practical problems, we can actively try to use the knowledge and methods we have learned from the perspective of mathematics to find strategies to solve problems; Facing the new mathematical knowledge, we can actively look for its realistic background and explore its application value. "(Mathematics Curriculum Standard) Students should not only understand the questions raised in the classroom and master ready-made mathematics knowledge and skills, but also consciously use classroom methods to understand things around them, understand and deal with related problems, so that the knowledge they have learned becomes closely related to life and society, and truly make mathematics" come from life and apply it to life ". In this regard, teachers should fully be the guides and collaborators of students' "using mathematics".
For example, after learning the measurement of "statistical knowledge, price and shopping calculation, length, area, volume, etc.", we should provide students with practical opportunities as much as possible and guide them to apply mathematics to their lives. We can ask students to measure the length and width of the classroom; Measure the length and width of blackboard, desk and book; Measure the length and width of furniture and the height of mom and dad; Measure the weight of mom and dad; Calculate the price of goods purchased, such as shopping. In the course of "applying mathematics", we can experience the role of what we have learned, stimulate students' enthusiasm for learning, stimulate students' internal force to solve problems, and let students taste the pleasure of applying what they have learned.